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TOPIC 9-3: SIMILAR TRIANGLES When polygons are similar, two criteria must be met: 1) Corresponding angles are ____________________. 2) Corresponding sides are ___________________________. However…if you don’t know the measures of all sides and angles, is there another way to tell? There are several theorems that allow us to show that triangles are similar. AA Similarity ________________-________________ Similarity If two angles of one triangle are _____________ to two angles of another triangle, then the triangles are _________________. EXAMPLE 1 Can these triangles be proven similar by AA? If so, write a similarity statement. G J H F K YES or NO ∆_________∼ ∼∆___________ A second way to show that triangles are similar is: ________________-________________ -_____________ Similarity In two triangles, if a pair of corresponding angles is SAS _______ and the sides including the angle are Similarity __________________________, then the triangles are ______________________. EXAMPLE 2 Can the two triangles be proven similar by SAS? If Q so, write a similarity statement. L 9 6 M 120°° N 4 P YES or 120°° R 6 NO ∆___________ ∼∆___________ There is a third way to show that triangles are similar… ________________-________________ -_____________ Similarity SSS If all three pairs of corresponding sides of two triangles are _______________________, then Similarity the two triangles are _____________________. EXAMPLE 3 Are the triangles below similar by SSS? If so, write a X similarity statement. S T 9 4 3 5 U W YES or 12 15 NO ∆___________ ∼∆___________ V EXAMPLES Are the two triangles similar? If so, state how and write a similarity statement. X D 4. 5. 5 3 6 E 6 F G 10 W 80°° V 6 80°° Z Y H YES or NO YES HOW? or NO HOW? ∆________∼ ∼∆_________ 6. Q ∆________∼ ∼∆_________ T L 7. 10 6 6 18 R K 3 S 8 5 N J U YES or V 24 NO YES HOW? or NO HOW? ∆________∼ ∼∆_________ 8. M ∆________∼ ∼∆_________ R P 12 3 YES or NO Q HOW? 4 L ∆________∼ ∼∆_________ 9 S EXAMPLES Are the two triangles similar, and if so what is the common ratio? 9. The measures of the sides of ∆ABC are 4, 5, & 7. The measures of ∆XYZ are 16, 20, & 28. 10. ∆PQR has sides 3, 5, & 6. ∆STU has sides 2.5, 2, & 3.